Space within semiconductor particles

The space charge layer within semiconductor particles... 

The potential distribution, and hence the extent of the band bending, within the space charge layer of a planar macroscopic electrode may be obtained by solution of the one-dimensional Poisson-Boltzmann equation [95]. However, since the particles may be assumed to have spherical geometry, the Poisson-Boltzmann for a sphere must be solved. This has been done by Albery and Bartlett [131] in a treatment that was recently extended by Liver and Nitzan [125]. For an n-type semiconductor particle of radius r0, the Poisson-Boltzmann equation for the case of spherical symmetry takes the form ... 

In most metals the electron behaves as a particle having approximately the same mass as the electron in free space. In the Group IV semiconductors, dris is usually not the case, and the effective mass of electrons can be substantially different from that of the electron in free space. The electronic sUmcture of Si and Ge utilizes hybrid orbitals for all of the valence elecU ons and all electron spins are paired within this structure. Electrons may be drermally separated from the elecU on population in dris bond structure, which is given the name the valence band, and become conduction elecU ons, creating at dre same time... 

An important consideration for the electronics of semiconductor/metal supported catalysts is that the work function of metals as a rule is smaller than that of semiconductors. As a consequence, before contact the Fermi level in the metal is higher than that in the semiconductor. After contact electrons pass from the metal to the semiconductor, and the semiconductor s bands are bent downward in a thin boundary layer, the space charge region. In this region the conduction band approaches the Fermi level this situation tends to favor acceptor reactions and slow down donor reactions. This concept can be tested by two methods. One is the variation of the thickness of a catalyst layer. Since the bands are bent only within a boundary layer of perhaps 10-5 to 10 6 cm in width, a variation of the catalyst layer thickness or particle size should result in variations of the activation energy and the rate of the catalyzed reaction. A second test consists in a variation of the work function of the metallic support, which is easily possible by preparing homogeneous alloys with additive metals that are either electron-rich or electron-poor relative to the main support metal. 

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